Question

In a random sample of 257 adult Orcas in the wild, there were 159 whose total body length was 28 feet or longer. Create a 98% confidence interval for the population proportion of adult Orcas in the wild who total body length is 28 feet or longer. Enter the lower and upper bounds for the interval in the following boxes, respectively. You may answer using decimals rounded to four places or a percentage rounded to two. Make sure to use a percent sign if you answer using a percentage.  

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 159 / 257 = 0.6187

1 - = 0.3813

Z/2 = 2.326

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.326 * [(0.6187 * 0.3813) / 257]

= 0.0705

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.6187 - 0.0705 < p < 0.6187 + 0.0705

0.5482 < p < 0.6892

Lower bound = 0.5482

Upper bound = 0.6892